Research On Nonlinear Optimization Design Of Pendulum Tuned Mass Damper

Damper Pendulum Tuned Mass damper is a kind of Tuned Mass damper,which is widely used in practical engineering and can effectively reduce the response of structure under earthquake and wind loads.Under large response,PTMD shows nonlinearity,and the nonlinear effect brought by large swing Angle of PTMD will reduce its vibration control performance.In previous studies on PTMD,the equivalent linearization of swing Angle will overestimate its vibration control performance.Therefore,this paper studies the nonlinear design of PTMD.The energy response of the PTMD-structure nonlinear system under different optimization parameters is compared and analyzed.The main research work of this paper is as follows:（1）The PTMD-structure nonlinear system model is established,the motion equation of the nonlinear model is derived according to the Lagrange equation,and the frequency response function of the PTMD-structure nonlinear model under seismic excitation and wind excitation is derived based on Krylov-Bogoliubov slow variable parameter method.The Newmark-βnumerical method is used to verify the derived frequency response function,which shows that the frequency response function of the nonlinear model derived from the slow variable parameter method is feasible.（2）Compared and analyzed the frequency response of PTMD-structure nonlinear model and equivalent linearized model under different working conditions,and studied the influence of mass ratio of PTMD to structure and damping ratio of main structure on the nonlinear effect of PTMD.With the increase of excitation amplitude,the nonlinear effect will be enhanced,and the frequency response error of the two models is up to 59.98%.The nonlinear effect decreases with the increase of mass ratio and main structure damping.The parameters of PTMD in the PTMD-structural nonlinear model were optimized based on H₂criterion and H_∞criterion respectively,and the optimal design parameters of PTMD under different excitation amplitudes were obtained.Compared with the optimal parameters derived from the equivalent linear model,the structural response amplitudes could be effectively reduced.Under the action of large excitation,the structural response amplitude under the first two optimal parameters can be reduced by 40%-50%at most.（3）A high-rise office structure is taken as the research object,and its parameters are optimized by considering the nonlinear effect.The time-history response of the structure under the actual earthquake load is analyzed,and the time-history response of the structure under different optimization parameters is compared.It is found that considering the nonlinear effect to optimize the parameters of PTMD can effectively improve its damping rate.Compared with the optimal parameters of the equivalent linearized model,the PTMD damping rate increases by nearly 10%under the H₂optimization and H_∞optimization parameters,and the peak value of PTMD swing Angle decreases by 10%～20%under the multiple-event and earthquake-proof conditions,which indicates that the parameter optimization of PTMD based on the frequency response function derived from the nonlinear model can improve the damping rate of PTMD.Better structural displacement control is achieved with smaller swing Angle.（4）From the perspective of energy,the energy balance of PTMD-structural linear system and PTMD-structural nonlinear system under the action of earthquake is analyzed,which more intuitively shows the energy distribution and transformation in the structural system,and can consider the energy accumulation process of the structure in the range of earthquake duration.The difference of cumulative energy and instantaneous energy response between PTMD-structural nonlinear system and PTMD-structural linear system is compared and analyzed.The nonlinear factors will increase the total input energy of PTMD-structural system and the total damping energy of main structure.The energy response of PTMD-structural nonlinear system under earthquake action is compared and analyzed when the optimal parameters of Gerges optimization,H₂optimization and H_∞optimization are taken as the design parameters of PTMD.The parameter optimization of PTMD according to the PTMD-structural nonlinear system can reduce the energy input to the structure and reduce the total damping energy of the main structure.